You should be able to see the symbol animation as well as the main timeline animation.
One thing to check is if you are out of Symbol editing mode.
You get into Symbol editing mode by double clicking the symbol and while IN editing mode (Purple band on timeline) you can only see the animation in the symbol.
Think of a Symbol as a Movie within a Movie.
The Main Hype document has it's own timeline(s).
A Symbol has it's own timeline(s)
The main Hype timeline sees the Symbol as an Object that can be called upon when necessary.
But the Symbol has it's own set of timelines.
To view all the timelines in action you need to be in the Main timeline. NO Purple band.
And yes you will not see the timeline action play out in hype. You will need to preview.
Here is a video of the symbol timeline and the main working together in Hype.
and the updated looping symbol file so that you can see how it is constructed.
looping symbol2.zip (18.5 KB)